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124 DIOPTRICS.
Fig. For then RD rr RP 4- PD rr 2PD, and DF rr
73# Dp -FpF rr zDp zz 2DP.
PROP. XXIV.
75' An oblique pencil of rays SAGC, has its focus G
a little nearer the lens, than a direct pencil RAFC.
For if DS rr DR, then the angle CSA will be
fomething lefs than the angle CRA ; and upon
that account the rays SA, SC, will be fooner
brought to interfect at G, than the rays RA, RC,
do at F. But further, the rays RA, RC, falling
very nearly perpendicular to the fides of the lens
AC, HN, are lefs bent, than the rays SA, SC,
which fall obliquely on both fides the lens. For
the more oblique they are, the more they are bent,
and turned out of their direct way. And confequently the oblique rays SA, SC will fooner interfect in G, than thofe at F. But fince the angle
RDS is generally very fmall, the difference between DF and DG will likewife be very fmall.
Cor. 1. The focus of an oblique pencil, by afinglc
refratlion is nearly at the fame diftance as of a direct
pencil.
For in both cafes the extreme rays will interfect
the ray which paffes thro5 the center of the furface
AC, at the fame diftance.
Cor. 2. This Prop, holds good in a concave lens,
and alfo in a menifcus, as well as in a convex one.
For in all cafes the more oblique the rays are
the more they are bent, and the fooner they will interfect a direct ray paffing thro5 D the center of the
lens, by Cor. 2. Prop. XVII. But I endeavour to
avoid drawing a multiplicity of figures.
PROP.

124 DIOPTRICS.
Fig. For then RD rr RP 4- PD rr 2PD, and DF rr
73# Dp -FpF rr zDp zz 2DP.
PROP. XXIV.
75' An oblique pencil of rays SAGC, has its focus G
a little nearer the lens, than a direct pencil RAFC.
For if DS rr DR, then the angle CSA will be
fomething lefs than the angle CRA ; and upon
that account the rays SA, SC, will be fooner
brought to interfect at G, than the rays RA, RC,
do at F. But further, the rays RA, RC, falling
very nearly perpendicular to the fides of the lens
AC, HN, are lefs bent, than the rays SA, SC,
which fall obliquely on both fides the lens. For
the more oblique they are, the more they are bent,
and turned out of their direct way. And confequently the oblique rays SA, SC will fooner interfect in G, than thofe at F. But fince the angle
RDS is generally very fmall, the difference between DF and DG will likewife be very fmall.
Cor. 1. The focus of an oblique pencil, by afinglc
refratlion is nearly at the fame diftance as of a direct
pencil.
For in both cafes the extreme rays will interfect
the ray which paffes thro5 the center of the furface
AC, at the fame diftance.
Cor. 2. This Prop, holds good in a concave lens,
and alfo in a menifcus, as well as in a convex one.
For in all cafes the more oblique the rays are
the more they are bent, and the fooner they will interfect a direct ray paffing thro5 D the center of the
lens, by Cor. 2. Prop. XVII. But I endeavour to
avoid drawing a multiplicity of figures.
PROP.